Let Charu has x coins

Number of coins which Varun has = = =

Number of coins which Arun has = = =

Therefore, required percentage = = = 3.38%

Hence, option C is correct.

Divisibility of 9:- Sum of digits of a number is multiple of 9 or divisible by 9 then the number is divisible by 9.

Sum of digits of 34278A2597 = 3 + 4 + 2 + 7 + 8 + A + 2 + 5 + 9 + 7 = 47 + A

Multiple of 9 which is greater than 47 is 54

So,

47 + A = 54

A = 54 – 47 = 7

⇒ x⁵ - 10x⁴ + 11x³ - 10x² + 10x + 7

= x⁵ - 9x⁴ - x⁴ + 9x³ + 2x³ - 10x² + 10x + 7

=x⁵ - x⁵ - x⁴ + x⁴ + 2x³ - 9x² - x² + 9x + x + 7

=2x³ - x³ - x² + x² + x + 7

= x³ + x + 7

= 729 + 9 + 7

= 745.

Given Amount= Rs 8340

Principal=Rs 6000

Interest = Amount- Principal=Rs (8340-6000)

= Rs 2340

Interest=

2340 =

K=3

Given,

∠ACB = 116°

So, angle made by chord AB on major arc = 180° – 116° = 64°

So, ∠AOB = 2 × 64° = 128°

Now, ∠DAO = ∠DBO = 90° (angle made by tangents)

In quadrilateral DAOB

∠DAO + ∠AOB + ∠OBD + ∠BDA = 360°

⇒ 90° + 128° + 90° + ∠BDA = 360°

⇒ ∠BDA = 360° – 308°

⇒ ∠BDA = 52°

Hence, the correct answer is option D

We know that:

Diagonal of a cube =

⇒ 8  =

⇒ Side = 8 cm

Volume of the cube =

=

= 512 cm³

Hence, option C is correct.

A.T.Q.:

Perimeter of circle will be equal to the perimeter of the square.

⇒ 2×π×R = 4a (R = radius of the circle and a = side of square)

⇒ 2× (22/7) × 14 = 4 ×a

⇒ a = 22 cm.

Now, 

⇒ 2 × π × r × h = 4 × 22 (r & h = radius and height of the cylinder)

⇒ 2 × (22/7) × r × 2 = 88
⇒ r = 7 cm

Now, Required ratio is (7 + 2) : (7 − 2) = 9:5

Factors of 132 = 2 × 2 × 3 × 11

A number will be divisible by 132 if it is divisible by 2, 3 and 11.

From the given number,

Divisibility of 2 - A number is divisible by 2 if the last digit are 0,2 4, 6, 8.

Out of the given numbers 660, 754, 924, 1452, 1526, 1980, and 2170 are divisible by 2.

Divisibility of 3 - A number is divisible by 3 if the sum of the digits of the number is divisible by 3.

Out of the remaining numbers 660, 924, 1452, and 1980 are divisible by 3.

Now, all these numbers are divisible by 11.

Hence, 660, 924, 1452, and 1980 are divisible by 132.

Hence, option D is the correct answer.

Total number of marbles = 6 + 8 + 4 + 3 = 21

Favourable outcomes = 8 + 3 = 11

Probability = favourable outcome/total outcome

=

"Hence, option B is the correct answer."

(−12) [11 + {7 × (−3)}] ÷ [4 {13 − (−3) × (−6)}]

= (−12) [11 + {−21}] ÷ [4 {13 − 18}]

= (−12) [−10] ÷ [4 × {−5}]

= (−12) [−10] ÷ [4 × {−5}]

= 120 ÷ [−20]

= −6

Ranking of ten students in two subjects mathematics and statistics:

Coefficient of rank correlation

R =

= 1 – 1.3 = -0.3

Selling price at 25% profit = ₹ 10,000

Cost price =

=  = ₹ 8,000

Selling price at profit of 40% = 8000 + 40% of 8000

=

= 8000 + 3200 = ₹ 11,200

Time taken by Y to complete the work = 18/2 = 9 days

Let the total work be 18 units(LCM of 18 and 9).

Efficiency of X = 18/18 = 1 unit/day

Efficiency of Y = 18/9 = 2 units/day

Work done by X and Y in 1 day = 1 + 2 = 3 units

Required part = 3/18 = 1/6 Part

"Hence, option D is the correct answer."

LCM (6, 5) = 30

The required number will be given by = 30K + 1 

Here, 30K + 1 < 100 …….( as we require largest two digit number )

Putting K = 3,

⇒ 30×3 + 1 = 91 

Hence the number is 91.